In a method for controlling interface level between a liquid inventory and an overlying steam chamber in a subterranean petroleum-bearing formation, an inflow relationship is developed to predict the vertical position in a gravity field of the interface between the two fluids (liquid and steam) with a density contrast relative to a horizontal producer well. The inflow relationship is applied to producer well completions by designing the completion to raise or lower sand face pressures according to mobility variations over the horizontal length of the well. This pressure distribution will affect liquid levels according to the inflow relationship. The completion can include tubing-conveyed or liner-conveyed flow control devices to create flow network that provides a customized sand face pressure distribution. Axial flow relationships between adjacent locations along the producer well may be modeled in order to develop an axial flow network to facilitate estimation of liquid levels at selected locations.